頁籤選單縮合
題 名 | ARCH族模型估計與檢定的問題=A Problem in Estimation and Hypothesis Testing in ARCH Family |
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作 者 | 林建甫; 張焯然; | 書刊名 | 經濟論文叢刊 |
卷 期 | 24:3 1996.09[民85.09] |
頁 次 | 頁339-355 |
分類號 | 553.01 |
關鍵詞 | 人造輔迴歸式; 斜率外積; LM檢定; BHHH演算法; ARCH parameters; Auxiliary regression; Lagrange multiplier test; Outer-product-of-the-gradient; BHHH algorithm; |
語 文 | 中文(Chinese) |
中文摘要 | 本文探討人造輔迴歸式(artificial regression)與ARCH族模型估計、檢定的 關係及檢定引出的問題,我們先把Scoring及BHHH演算法中估計參數時遞迴更新 的方向同量(direction vector)化成人造輔迴歸式並且指出LM(Lagrange multiplier)檢 定的統計量與這人造輔迴歸式的關係。我們進而說明三種ARCH模型的LM檢定; 一是由一階微分的score函數出發的測驗;二是由Breusch和Pagan(1979)及 Koenker(1981)的推導,簡化的TR2(丁為樣本點個數)檢定統量;三是Bollerslev(1986) 提出用BHHH演算法以斜率外積(outer product of the gradient;OPG)作為訊息矩陣的 基礎,經由第一次OLS輔迴歸造出的TR2的統計量;其極限分配是一樣的。我們也 發現最常用的第三種檢定統計量,在小樣本下會有高估的情形。這與文獻上使用 OPG的檢定在平均數上有過度拒絕虛無假設的問題相同。這將建議一般對ARCH 族模型估計與檢定使用BHHH演算法的學者,要小心的使用BHHH演算法的檢定 結果。 |
英文摘要 | We express the direction vectors as auxiliary regressions and pointout how to take advantage of these auxiliary regressions to generate LM (Lagrange multiplier) test statistics. We test three LMtests which are asymptoticly equivalent but with different behaviors in small samples. The three LM tests are, the one with scorefunction and an information matrix; the TR@ version of Breuschand Pagan (1979) and Koenker (1981) and the TR@ version usingouter-product-of-the-gradient (OPG) in the first BHHH iterationin Bollerslev (1987). We find the third test rejects too often underthe null hypothesis. The reason is that when using the OPG toapproximate the Hessian, it produces a larger test statistic. This issimilar to the problem of applying OPG to a mean equation, butthis has not been noted in the variance equation. This suggests awarning for those who use the BHHH algorithm to generate LMtest statistics and find significant ARCH effects. |
本系統中英文摘要資訊取自各篇刊載內容。